Consider a market where there are two types of consumers. Each type of consumer demands zero or one unit of some good produced by the monopolist. The difference is, one type of consumer is willing to pay $10 for the good whereas the other type is only willing to pay $2 for the good. Suppose there are N > 2 number of consumers in the market and the cost to produce each unit of good is $1.
(a) If the monopolist can distinguish between one type of consumer over another, determine the profit maximizing outcome.
(b) Calculate the social surplus generated when the monpolist is able to distinguish between the two types of consumers.
(c) If the monopolist cannot distinguish between one type of consumer over another but believes that half the consumers are one type and the other half are another, determine the profit maximizing outcome.
(d) Calculate the the social surplus generated when the monopolist is unable to distinguish between the two types of consumers.